Uncovering the hydride ion diffusion pathway in barium hydride via neutron spectroscopy

Solid state materials possessing the ability for fast ionic diffusion of hydrogen have immense appeal for a wide range of energy-related applications. Ionic hydrogen transport research is dominated by proton conductors, but recently a few examples of hydride ion conductors have been observed as well. Barium hydride, BaH2, undergoes a structural phase transition around 775 K that leads to an order of magnitude increase in the ionic conductivity. This material provides a prototypical system to understand hydride ion diffusion and how the altered structure produced by the phase transition can have an enormous impact on the diffusion. We employ quasielastic and inelastic neutron scattering to probe the atomic scale diffusion mechanism and vibrational dynamics of hydride ions in both the low- and high-temperature phases. Jump lengths, residence times, diffusion coefficients, and activation energies are extracted and compared to the crystal structure to uncover the diffusion pathways. We find that the hydrogen jump distances, residence times, and energy barriers become reduced following the phase transition, allowing for the efficient conduction of hydride ions through a series of hydrogen jumps of length L = 3.1 Å.


Experimental Details
Quasielastic Neutron Scattering: QENS measurements were performed using the backscattering spectrometers BASIS 1 at Oak Ridge National Laboratory and HFBS at the National Institute of Standards and Technology (NIST). 2 Data was collected in two different experiments: (1) closed cycle refrigerator (CCR) at HFBS and (2) using a vacuum furnace at BASIS. All sample handling was performed in a helium glove box to avoid exposure to atmospheric water and oxygen. Cylindrical titanium sample cans were used at HFBS with gold O-ring seals. At HFBS, 1.5 g of BaH2 was loaded into an aluminum foil packet before being loaded into the titanium sample can. At BASIS, the sample was measured in a 5 mm diameter quartz NMR tube with m = 0.97 g of sample and measured under a helium gas atmosphere maintained at atmospheric pressure. Two different measurement configurations were used at BASIS using the Si(111) and Si(311) analyzers. The Si(111) analyzers provide an accessible Q-range from 0.2 to 2.0 Å -1 , an energy range of ± 100 µeV, and an energy resolution of FWHM = 3.5 µeV. The Si(311) analyzers provide an accessible Q-range from 0.4 to 3.8 Å -1 , an energy range of ± 740 µeV, and an energy resolution of FWHM = 15 µeV. At BASIS, the instrumental resolution function was measured at T = 300 K. Shorter measurements for the elastic intensity scan were taken every 10 K between 300K and 880 K while longer scans with higher statistics suitable for detailed QENS data analysis were measured between 340 K and 920 K. At HFBS, measurements were conducted using the standard instrument configuration with an accessible Q-range from 0.25 to 1.75 Å -1 , an energy range of ± 16 µeV, and an energy resolution of FWHM = 0.8 µeV. Empty vanadium cans were used to measure the instrumental resolution function. Empty can subtractions were performed for the HFBS measurements but not for BASIS. We have performed empty can measurement at BASIS with a similar sample environment set up at a number of temperatures and could not observe any visible QE contribution. However, empty can subtraction could help to distinguish any wide, flat, or low intensity components that are seemingly part of the background. Thus, it is possible that we would have missed such a QE component.
Inelastic Neutron Scattering: Vibrational spectroscopy measurements were performed at VISION at ORNL. 3 VISION is highly sensitive to hydrogen displacements and has an accessible energy range from the elastic limit up to 500 meV with an energy resolution of ∆E/E ≈ 1-2% across the entire energy range. For the low temperature measurements between 5 K and 300 K, a 0.53 g BaH2 sample was measured in an 8 mm diameter vanadium PAC can in a CCR. Higher temperature measurements from 300 K to 650 K were measured using a cylindrical stainless-steel sample can with a copper O-ring seal. The sample (m = 1.4 g) was suspended in an annular copper foil packet. Data reduction was performed using Mantid. 4 Empty sample holders were measured at various temperatures and subtracted from the data.
Neutron Powder Diffraction: NPD measurements were performed at NOMAD at ORNL. 5 BaD2 was measured at 850 K in a vacuum furnace. A 0.925 g sample was loaded into a 5 mm diameter quartz NMR tube. An empty sample holder was used for background subtraction. S2 function R(Q,E). B(Q,E) is the linear background term. Only one quasielastic process is observed at HFBS and BASIS: at HFBS, the motion corresponds to the slower diffusion process in the orthorhombic phase while the quasielastic process observed at BASIS corresponds to the faster diffusion process in the hexagonal phase. Therefore, this data is fit with a single Lorentzian model, where Γ is the Lorentzian half-width at half-maxima (HWHM).
The Lorentzian broadening at low momentum transfers follows the characteristic DQ 2 dependence associated with longrange translational diffusion. At higher Q, the broadening deviates from the DQ 2 dependence, which yields information about the nature of the diffusion process. Different jump-diffusion models were tested, as shown in Fig. 3 in the main text. The Chudley-Elliott jump diffusion model 6,7 best describes the QENS data, where L is the jump length and τ is the residence time. In this model, the particle resides in the same average position, only undergoing thermal oscillations about this lattice site. After remaining in that position for a characteristic residence time (τ), the particle jumps over a discrete distance to another available site. The diffusion coefficient for the Chudley-Elliott model can be calculated using the following equation. 6,7 = 2 6 ( 4) After plotting the obtained diffusion coefficients in an Arrhenius format, the Arrhenius equation was applied to obtain activation energies, Ea, and the temperature independent preexponential diffusion coefficient, D0.
The QENS data fits were performed using the QCLIMAX package within ICE-MAN, the Integrated Computational Environment-Modeling & Analysis for Neutrons. ICE-MAN has been recently developed at ORNL for analysis of neutron scattering data. The unconstrained initial fits showed a clear Chudley-Elliott diffusive behavior. Therefore, the Lorentzian widths were further constrained to follow the Chudley-Elliott model of equation (S3) (comparison of fits with DAVE and QCLIMAX are shown later). The software fits the QENS spectra at every Q value simultaneously, effectively fitting Sqe(Q,E) to the following quasielastic model and determining by minimization the parameters L and τ.

Comparison of DAVE vs. QCLIMAX
A comparison of the Q-dependence of the Lorentzian widths fit with QCLIMAX vs. DAVE 10 is shown in Fig. S1. DAVE was used to fit each Q value individually with equation (S1) and the Lorentzian width was extracted from these fits (black circles). The resulting widths were then fit manually with the Chudley-Elliott model, equation (S3) (black line). Next, the global fitting procedure (Eq. S7) that uses QCLIMAX to fit the entire range of Q-values simultaneously to the Chudley-Elliott model was applied (red line). The fit of the Chudley-Elliott model is almost identical with respect to QCLIMAX and DAVE for the 750 K data. The errors calculated with QCLIMAX are noticeably smaller which yields more accurate jump lengths and residence times. The benefits of QCLIMAX becomes apparent for the 670 K data, which is far more difficult to analyze due to the smaller quasielastic intensity and narrower broadening. By constraining the fitting algorithm to follow a Chudley-Elliott behavior, QCLIMAX can produce an excellent fit of the data that also agrees well with the widths obtained in the DAVE fits.
A comparison of the fit results from QCLIMAX for an unconstrained fit vs. a fit constrained to follow the Chudley-Elliott jump diffusion model is shown in Fig. S2 for T = 850 K. The unconstrained fit yields widths that follow a clear Chudley-Elliott  relationship. The jump lengths and residence times extracted from the fits are also displayed in Fig. S2. Clearly, the errors are reduced using the constrained fit. Both the unconstrained and constrained fits yielded similar results, verifying that the assumptions in our global fitting procedure are justified and serve to increase the accuracy of our results.

HFBS Spectra Comparison
In the main text, it was mentioned that a quasielastic broadening was first observed around 600 K, but that the width was too narrow compared to the instrumental resolution to be reliably extracted. This can be observed in Figure S3, where the 600 K spectrum exhibits a slight broadening and continuously broadens with increasing temperature. The Lorentzian widths can first be reliably extracted beginning with the 670 K measurement. All the spectra in Figure S3 are normalized to unity (with respect to the elastic peak) to demonstrate the amount of quasielastic broadening with temperature.

INS Temperature Dependence
The temperature dependence of the H(1) and H(2) optical modes are shown in Figure S4. This was calculated by integrating the peak intensities over the entire H(1) and H(2) mode regions (H(2): 55-85 meV, H(1): 86-125 meV) across the temperature range of 5-650 K. Lastly, a 2nd order polynomial was applied to obtain a general fit of the data to quantify the temperature dependence of the optical modes, as shown as solid lines of Figure S4. As can be observed, the lower energy H(2) modes lose intensity faster at lower temperatures, but at higher temperatures both the H(1) and H(2) modes experience similar behavior. The H(2) modes follow this trend at a lower temperature of approximately 70 K compared to the higher energy H(1) sites. This can be interpreted that the H(2) sites would likely gain enough energy to overcome the thermal barriers for diffusion at a lower temperature compared to the H(1) sites. Figure S3. QENS spectra measured at HFBS over a temperature range of 600 -750 K. The resolution function was measured at ambient conditions using a vanadium can.